Max-Planck- Inst Itut für WIssenschaftsgeschIchte

Max Planck Institute for the History of Science

2009

PrePrInt 371

Larrie D. Ferreiro

the aristotelian heritage in early naval architecture, from the Venetian arsenal to the french navy, 1500–1700

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THE ARISTOTELIAN HERITAGE IN EARLY NAVAL

ARCHITECTURE, FROM THE VENETIAN ARSENAL TO THE

FRENCH NAVY, 1500–1700

ABSTRACT

Naval architecture has been at the center of some of the earliest studies of rational

mechanics investigated during the Scientific Revolution, but until recently has received

scant attention from scholars. In particular, there has been little exploration of the

Aristotelian roots of the mechanics of naval architecture. For example, several

investigations of oared galley design in the Venetian Arsenal during the 1500s were

derived directly from study of the Aristotelian treatise Mechanical Problems. This

treatise, along with Aristotle’s conception of buoyancy, became the basis for further work

on naval architecture by Renaissance and Jesuit mathematicians during the sixteenth and

seventeenth centuries. The culmination of this Aristotelian heritage is found in the works

of the French navy professor Paul Hoste who developed the first synthetic works of naval

architecture at the end of the seventeenth century, just as Newtonian mechanics began its

ascent towards wider acceptance.

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1. INTRODUCTION

Naval architecture has played a small but strategically vital role in the development of

rational mechanics, yet until lately it has received scant attention from historians. Recent

works on the development of naval architecture during the Scientific Revolution have

focused on its origins in Archimedes’ theorems for displacement and stability.1 Yet some

of the first theoretical problems in naval architecture, systematically analyzing important

mechanisms such as rowing, the action of sails and buoyancy, actually appeared more

than a century earlier in the works of the school of Aristotle. When a series of Latin

translations were made during the sixteenth century of the Aristotelian treatise

Mechanical Problems, many of these concepts were analyzed and even directly employed

by scientists working in the late Renaissance and the beginnings of the Scientific

Revolution. By the end of the seventeenth century these theories were being applied

across the full range of ship problems; but by then Archimedes’ theories had begun to

displace Aristotle, leading to the modern system of naval architecture.

1 See for example: Horst Nowacki, “Archimedes and Ship Stability”, in Proceedings of the Euroconference on "Passenger Ship Design, Operation and Safety", edited by Apostolos Papanikolaou and Kostas Spyrou (Athens: NTU, 2001); reprinted as MPIWG Preprint 198 (Berlin, Max Planck Institute for the History of Science, 2002); and Horst Nowacki and Larrie Ferreiro, “Historical Roots of the Theory of Hydrostatic Stability of Ships”, in Proceedings of the 8th International Conference on the Stability of Ships and Ocean Vehicles, edited by Luis Pérez Rojas (Madrid: ETSIN 2003, pp. 1–30); reprinted as MPIWG Preprint 237 (Berlin, Max Planck Institute for the History of Science, 2003).

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2. THE ORGINS OF ARISTOTELIAN NAVAL ARCHITECTURE IN THE MECHANICAL PROBLEMS, c. 300 BC– c. 15 BC

In none of the known writings of Aristotle (384 BC–322 BC) did he deal with mechanics

per se, in the sense of the application of physical principles to machines, but rather he

discussed the more general principles of causality and change. In his Physics, for

example, Aristotle described physical change as being proportional to the “power” of an

agent of change multiplied by the time of the change; but this concept was not merely

applicable to mechanical elements such as a change of position, but also to changes of

state (weight) or chemistry (heating).2 The application of these general mathematical

principles to the specific subject of mechanics was made in the short treatise Mechanical

Problems (also called Mechanical Questions, Questions of Mechanics or Mechanica)

apparently written after his death by a member of his Peripatetic school, circa 300 BC.

Although the authorship of the work remains in dispute, it is usually described as

“Aristotelian” or “pseudo-Aristotelian”.3 Mechanical Problems was in fact a textbook of

35 practical problems in the form of short questions followed by extensive answers,

describing how specific devices or techniques allow a greater force to be overcome by a

lesser one by application of the principle of the lever.4 Of these problems, four were

2 Aristotle, Physics, trans. Robin Waterfield (Oxford: Oxford University Press, 1999); VII 5, 249b7 – 250a25 at pp. 182–183; Edward Hussey, “Aristotle’s Mathematical Physics: A Reconstruction” in Aristotle’s Physics: A Collection of Essays, ed. Lindsay Judson (Oxford: Clarendon Press, 1991) pp. 213–242, at pp 215–216. 3 Aristotle, Minor Works, trans. Walter S. Hett (Cambridge, MA: Harvard University Press, 1963) pp. vii–viii. A recent study by Thomas Winter argues that Mechanical Problems was authored by Archytas; see Thomas Nelson Winter. The Mechanical Problems in the Corpus of Aristotle (Lincoln: University of Nebraska, 2007), http://digitalcommons.unl.edu/classicsfacpub/68, accessed March 2009. 4 Peter Damerow, et al., “Mechanical Knowledge and Pompeian Balances”, in Homo Faber: Studies on Nature, Technology and Science at the Time of Pompeii, eds. Jürgen Renn and Giuseppe Castagnetti (Rome: “L’Erma” di Bretschneider, 2002), pp. 93–108, at p. 94.

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directly concerned with issues of naval architecture: two with rowing by oars; one with

steering by rudder; and one with the interaction of the sail and mast.

Mechanical Problems began with a discussion of the lever, declaring that its first

principle is based on the circle, on the grounds that the line of the circumference moves

backwards and forwards simultaneously, thereby accounting for the movement of the

opposite ends of a lever. The first three problems in the treatise establish the basic theory

of the lever, derived from Aristotle’s argument in Physics that physical change is a

function of the “power of change” multiplied by the time of the change. In Mechanical

Problems, the law of the lever was expressed as a dynamic proportion, the product of the

weight and speed being equal on either side of a fulcrum (using modern algebraic

formulation, force and velocity are equal: Fv = fV).5 This is in contrast to the modern,

statical concept of the lever, first rigorously elucidated by Archimedes of Syracuse (c.

287 BC – c. 212 BC) in his Equilibrium of Planes, that the products of the force times

length are equal (Fl = fL) on either side of a fulcrum.6 A comparison of the two is shown

in Figure 1.

5 Aristotle, Mechanical Problems 848b – 850b (in Minor Works, pp. 330–355). The employment of the circle as the fundamental principle of mechanics is explored in Christiane Vilain, “Circular and Rectilinear Motion in the Mechanica”, in Mechanics and Natural Philosophy before the Scientific Revolution, ed. Walter Roy Laird and Sophie Roux (Dordrecht, Spinger 2008) pp. 149–172. 6 Archimedes and Thomas Little Heath, The Works of Archimedes (New York: Dover Publications, 2002), pp. 238–239.

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Figure 1

Lever laws in the Aristotelian Mechanics and Archimedes’ Equilibrium of Planes

This principle of the lever formed the basis for the questions discussed in Mechanical

Problems, including the four concerned with naval architecture, as follows:7

4) Q: Why do the rowers in the middle of the ship (i.e., amidships) contribute the most to

its movement? A: The oar acts a lever with the thole-pin (i.e., oarlock) as the fulcrum, the

moving weight (the rower) is on the inside of the ship, and the moved weight (the sea) is

on the outside. Since the ship is widest at the middle, more of the oar is on the inside, so

the movement of the oar against the thole-pin causes the pin (and therefore the ship) to

move forward the greatest distance.

5) Q: How can the rudder, which is small and at the end of the ship, move the entire

vessel so easily with a short tiller and the strength of just one man? A: As with the oar,

the tiller is the lever, and the rudder pushes against the sea. Because it is at the end of the

ship, the rudder can move faster and thus cause the ship to turn. (There is then a further

explanation of why an oar does not rotate precisely around the thole-pin, but rather at a

7 Aristotle, Mechanical Problems 850b – 851b (in Minor Works, pp. 355–361); Thomas Little Heath, Mathematics in Aristotle (Oxford: Clarendon Press, 1949) pp. 237–239.

Aristotle: F v = f V

V F f

v F f

Archimedes: F l = f L

l L

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point further away from the rower, because the ship moves forward a greater distance

than the oar moves backwards, thus displaces the fulcrum.)

6) Q: Why does a sail attached to a higher yardarm push a ship faster than if the same sail

were attached to a lower yardarm? A: The base of the mast is the fulcrum, so the higher

the yardarm, the more rapidly it can move for a given force.

7) Q: Why, when running before the wind, do sailors take in sail at the stern and let it out

at the bow? A: More sail at the bow turns the ship away from the wind, and less sail at

the stern allows the rudder push against the sea.

Thus, the mathematical mechanics of Aristotle and his followers were aimed at

describing, in a qualitative sense, the laws of proportionality behind the actions of certain

simple machines; for the problems in question, the proportion between force and speed

across a lever.8 The Mechanical Problems became known to the Romans through the Ten

Books on Architecture of Vitruvius (c. 80 BC – c. 15 BC) who also incorporated the

naval architectural questions in his explanations of machines.9 It should be noted that

these analyses were qualitative in nature, and did not provide measurable, quantitative

explanations for the physical processes of how a ship moves under oar and sail.

8 Hussey, “Aristotle’s Mathematical Physics”, pp. 215–220, 240–241. 9 Marcus Vitruvius Pollio, The Ten Books on Architecture, trans. Morris H. Morgan (Cambridge, MA: Harvard University Press, 1914) p. 292.

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3. THE VENETIAN ARSENAL AND THE APPLICATION OF MECHANICAL PROBLEMS TO PRACTICAL NAVAL ARCHITECTURE, 1517–1593

The rediscovery of the text of the Mechanical Problems at the dawn of the Scientific

Revolution sparked at least two attempts within the Venetian Arsenal to directly apply its

lessons to the design of oared vessels. Mechanical Problems appears to have been

unknown to European scholars throughout the Middle Ages.10 It was included in the

works of Aristotle that were typeset and published by the Venetian printer Aldus

Manutius from 1495–1498, part of a renaissance of Greek learning that quickly spread

through Europe.11 In 1517, the Venetian scholar and humanist Vettor Fausto was the first

to translate the treatise into Latin, although he did so without any commentary.12 Fausto

(1480 – c.1551) was a professor of Greek at the Scuola Grande di San Marco, which was

not a school in the modern sense of the word, but more of a meeting-place for both

secular and religious activities. He was one of a growing number of Venetian scholars at

the beginning of the sixteenth century to examine ancient military texts in order to assist

in the defense of the territory against their erstwhile Ottoman enemies. At that time, the

backbone of Venice’s navy was the trireme galley, a long, light ram-bowed warship with

three banks of oars, which was mass-produced at the sprawling Arsenal dockyard to the

east of the main square of San Marco. During his tenure at the Scuola, Fausto had

carefully examined Greek and Roman texts concerning naval warfare with oared ships, as

10 For an examination of the development of mechanics from the Middle Ages through the Renaissance, see especially Walter Roy Laird, “The Scope of Renaissance Mechanics”, Osiris 1986, 2/2 pp. 43–68; and his Introduction to The Unfinished Mechanics of Giuseppe Moletti (Toronto: University of Toronto Press, 2000) pp. 6–18. 11 Stillman Drake, “The Pseudo-Aristotelian Questions of Mechanics in Renaissance Culture”, in his Essays on Galileo and the History and Philosophy of Science (Toronto: University of Toronto Press, 2000) pp. 131–169, at p. 133.

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well as speaking with Venetian shipbuilders and ship masters, and mariners from many

other ports who came to the great city on the Adriatic. He came to the conclusion that the

Venetian trireme, which had one oarsman per oar, could be improved by adding a second

rower to each of the top two banks of oars, which was a common practice in Greece after

the end of the Peloponnesian wars in 404 BC. In August 1525 Fausto presented to the

Senate his model of a quinquereme, a 5-oarsman-per-tier galley, which he argued would

be more effective than the trireme.13

(It is here necessary to clarify some often-confusing terms. A trireme—triere in Greek—

is generally considered to be a ship with three vertically-arranged banks of oars for every

tier, or column of oars, along the side of the galley, normally with one oarsman pulling

each oar. The top oarsman was seated the furthest outboard, and the bottom two were

progressively further inboard. Modern research, using full-scale vessels as well as virtual

protoypes, has demonstrated that three banks of oars are the maximum number that can

be effectively arranged within a vertical tier. Thus, the term quinquereme did not refer to

the number of oars but rather the number of oarsman per tier; two each on the top two

tiers, and a single rower on the bottom.)14

12 Vettor Fausto, Aristotelis Mechanica, Victoris Fausti industria in pristinum habitum restituta ac latinitate donate (Paris: Jodocus Badius, 1517). Fausto’s first name is sometimes spelled “Vettore“ or given as “Victor“ or “Victoris“. 13 The story of Vettor Fausto and his development of the quinquereme is derived from: Frederic Chapin Lane, Venetian Ships and Shipbuilders of the Renaissance (Baltimore: Johns Hopkins University Press, 1934; reprint New York: Arno Press, 1979), pp. 64–71; Ennio Concina, L’Arsenale della Repubblica di Venezia: (Milan: Electa, 1984) pp. 108–134; Concina, Navis: L’umanesimo sul mare, 1470–1740 (Turin: Giulio Einaudi, 1990), pp. 70–90. 14 See John S. Morrison and Robert Gardiner (eds.), The Age of the Galley: Mediterranean Oared Vessels Since Pre-Classical Times (London: Conway Maritime Press, 2004) for a general overview of oared vessels; and John S. Morrison, John F. Coates and N. Boris Rankov, The Athenian Trireme: the history and reconstruction of an ancient Greek warship (Cambridge: Cambridge University Press, 2000) for a detailed explanation of the construction and mechanics of rowing multi-tiered oared vessels.

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Fausto was not a shipbuilder, so there was naturally a considerable uneasiness within the

Senate to spend the money and manpower on building a full-sized version of his model,

which would be both longer and wider than a standard trireme. However, since the only

unknown was his proposed arrangement of oarsmen, they voted him funds to build a

land-based model of his concept. When this showed that the oarsmen could row together

reasonably well, he was voted additional funds for material and allowed the use of an

Arsenal dock to build a full-sized quinquereme, which was completed in April 1529. It

won a race against a lighter trireme, though it was harder to maneuver. The concept was

not immediately accepted, but over the course of several decades the Arsenal built a

number of quinqueremes, which continued to be in service for the next forty years.

Indeed, a Fausto quinquereme was originally the flagship of Marcantonio Colonna, the

Italian admiral who later fought at the battle of Lepanto, before it was struck by lightning

and burned in October 1570 (a year before the battle) at Kotor in modern-day

Montenegro.15

The link between Fausto’s quinquereme and his translation of Mechanical Problems is at

best conjectural, but there is enough evidence to plausibly infer that he was at least

inspired by the ancient work to re-imagine how a galley could be improved. Problem 4, it

will be recalled, asked: “Why do the rowers in the middle of the ship contribute the most

to its movement?” The answer, according to the author who undoubtedly saw many war

15 Niccolò Capponi, Victory of the West: The Great Christian-Muslim Clash at the Battle of Lepanto (Cambridge, MA: Da Capo Press, 2007), pp. 147, 152. A letter in the Florence archives from Cosimo Bartoli, Venice ambassador to Florence, dated 15 June 1570, noted that Colonna’s quinquereme had been

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galleys, was that since the ship was wider amidships, more of the oar was inside the ship.

(It is here necessary to point out that the all the oars of a Greek galley were of about

equal length and arranged to form a straight line outside the ship, so the oars at amidships

were longer inboard than the ones at the narrower bow and stern.)16 The “lever law” here

assumes that the paddle entering the sea is fixed, so the fulcrum (thole-pin) moves

forward, pushing the ship forward. Fausto’s insight was to connect this law with the

ancient use of multiple oarsmen on each oar, which would be achievable by lengthening

the inboard reach of the oars, requiring a widening of the ship overall. In other words, the

benefit from using the Mechanical Problems was in the arrangement of oarsmen to

provide the greatest mechanical advantage on each oar, rather than depending solely on

the greater number of oarsmen. Fausto did not state any of this explicitly in his proposal

to the Senate, but late in his life he remarked that “having taken on the text of Mechanical

Problems for translation… it had enriched the design of every splendid machine”. A

contemporary of Fausto, Alessandro Zorzi, wrote some thirty years after Fausto’s death

that “the thing does not consist in the number of people, but rather how much of the oar is

within the galley, and how easy it is to row that oar; for as much as the inside and outside

of the oar are the same length from the fulcrum, the easier it will be to lever the largest

weight.”17

In 1545, after two decades of working on his quinquereme and other projects, Fausto had

began revising his translation of Mechanical Problems with additional commentary based

built by Fausto some thirty years earlier, but had never before been in the water (cited by Alberto Guglielmotti in Marcantonio Colonna alla battaglia di Lepanto (Florence: Felice Le Monnier, 1862) p. 25) 16 Morrison et al., The Athenian Trireme, pp. 137–138. 17 Concina, Navis, pp. 80–81, 166.

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on his experiences, and including drawings of various inventions. Colleagues who

viewed this now-lost manuscript asserted that it would have contributed greatly to the

architectural discipline; however, he died before he could complete it.18

The Venetian Arsenal was also the site of a second attempt to directly apply Aristotelian

mechanics to naval architecture, though with quite different results. The great Italian

mathematician and astronomer Galileo Galilei (1564–1642) had settled in Venice in

1592, and was immediately fascinated by the workings of the great shipyard. The

admiration was mutual, for soon after his arrival, one of the Commissioners of the

Arsenal, Giacomo Contarini (1536–1595), wrote him asking for advice on the placement

of oars in a galley. Contarini was no mere bureaucrat; a skilled observer, he had carefully

documented the manner of laying out and constructing galleys in two manuscripts that

circulated widely within the Arsenal.19 Contarini and his Venetian colleagues were, at the

time, attempting to build a more maneuverable fleet after the great victory at Lepanto in

1571, in order to meet the renascent threat from the Ottoman Empire. Contarini’s

question concerning the optimal position of oars and rowers for propulsion and

maneuverability caused Galileo to reflect upon the Mechanical Problems, in much the

way Fausto had done long before his birth. But his reading of the work led him to a

completely opposite conclusion: instead of placing more of the oar inside the vessel, as

Fausto evidently did, Galileo wrote back to Contarini suggesting that the inboard reach,

where the rowers sit, should be as short as possible, in order to move the vessel with

18 Enino Concina, “Humanism on the Sea”, in Mediterranean Cities: Historical Perspectives, ed. Irad Malkin and Robert L. Hohlfelder (Towata, NJ: Frank Cass, 1988), pp. 159–165, at p. 162. 19 Giacomo Contarini, Arte de far Vasselli, ca. 1590 and Del fabricar galere, 1592; Archivio Di Stato Di Venezia: Archivio proprio Contarini b.19 and b.25.

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greater force. Hearkening back to Figure 1, Galileo was insisting that Aristotle’s lever

law, Fv = fV, applies in this case, corresponding to a ship moving across a solid surface

with the oars acting as stilts; the force applied to a shorter inboard reach translates to a

faster movement of the oar blade through the water.

Contarini’s response to Galileo, written just a few days later, made it clear that the

scientist had not given careful thought to the practical aspects of Aristotelian mechanics,

and in fact this letter seems to have provided Galileo a catalyst for a complete

reexamination of the subject. The length and position of the oars have to be balanced,

Contarini explained, not only with regard to the limited human force of the rowers, but

also due to the structural limits of the oars themselves. A much longer oar on the outside

would break under the loading; and for it to be structurally resistant, the thickness would

have to increase so much that an oarsmen would no longer be able to move it. This

response by Contarini caused Galileo to reconsider his conception of mechanics and

begin examining the strength of materials. The results of this research would only be

published in his famous Two New Sciences some forty years later, where he

complimented the Arsenal workers on their expertise and analysis in the field of

mechanics.20

20 For an examination of the correspondence between Galileo and Contarini on the position of oars and Galileo’s subsequent foray into the strength of materials, see Jürgen Renn and Matteo Valleriani, Galileo and the Challenge of the Arsenal (Berlin: Max Planck Institute for the History of Science Preprint 179, 2001; reprinted in Nuncius, XVI/ 2, 2001, pp. 481–503). For other Aristotelian influences on Galilean mechanics, see William A. Wallace, Galileo, the Jesuits and the Medieval Aristotle (Brookfield, VT: Varorium, 1991) pp. 368–378.

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4. FURTHER ANALYSIS OF MECHANICAL PROBLEMS IN LATE RENAISSANCE MECHANICS, 1531–1669

About the time Fausto was building his quinqueremes in Venice, a Portuguese

mathematician named Pedro Nunes (1502–1578) was reinterpreting Aristotle’s works. As

a young professor and cosmographer at the University of Lisbon, he was principally

concerned with navigation, which at the time incorporated aspects of shipbuilding and

maneuver. Around 1531 he began using Fausto’s translation of Mechanical Problems in

his teachings, but quickly found flaws in the assumptions related to the oar problems.

Specifically, Nunes argued that the rowing motion involved not one but two types of

motion: the linear one of the ship, assumed by the original author; but also, overlaid on

that, the circular motion of the oar around the thole-pin. Using a series of geometrical

arguments, Nunes refuted the assertion made in Mechanical Problems that the thole-pin

acts as the fulcrum of the lever, which according to its author enabled the ship to move

further forward than the oar blade moves backward; rather, he stated, the blade of the oar

in the water is the actual pivot point (note that Nunes’ assertion is actually fairly close to

modern theories of rowing).21 Although justifiably proud of his rigorous analysis, he did

not publish his findings until thirty years later in 1566. Nunes’ results were reproduced

almost integrally by Henri de Monantheuil (1536–1606) in his own 1599 commentary on

21 Pedro Nunes, “In Problema mechanicum Aristotelis de motu nauigii ex remis Annotatio una”, in Petri Nonii Salaciensis Opera (Basil: Ex Officina Henricpetrina, 1566). Nunes’ work is extensively analyzed by Henrique de Sousa Leitão in O Comentário de Pedro Nunes à Navegação a Remos (Lisbon: Ediçôes Culturais da Marinha, 2002) and “Pedro Nunes and the Aristotleian Mechanical Problems”, in Petri Nonii Salaciensis Opera: Proceedings of the International Conference Lisbon-Coimbra 24–25 May 2002, ed. Luís Trabucho de Campos, Henrique de Sousa Leitão and João Filipe Querió (Lisbon: Universidad de Lisboa, 2003) pp. 141–182.

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Aristotle, and in 1615 by Giuseppe Biancani (1566–1624) in his Aristotelis loca

mathematica.22

The Italian mathematician and writer Bernardino Baldi (1553–1617) was the next to

elaborate on Mechanical Problems, beginning his commentary in the 1580s, though it

was only published posthumously in 1621. Using different geometrical principles, Baldi

also argued – as did Nunes – that the blade within the ocean is the fulcrum of the oar, not

the thole-pin. He then spent a considerable amount of time on Question 5 regarding the

action of the rudder. He apparently performed an experiment using a pontoon fixed by a

rope in a flowing river, in order to determine the course a ship would take when the

rudder was put over. He then analyzed Question 6 (regarding the height of the mast),

arguing that it is the same type of fulcrum as a claw-hammer; the higher the mast, the

more it pulls the stern up and the faster the ship goes. Baldi argued that constructors

cleverly place the mast forward of amidships in order to give it a greater lever arm, so as

to drive the ship faster.23

In 1627, the Italian theologian Giovanni di Guevara (1561–1641), a friend of Galileo,

published one of the most thorough commentaries on Mechanical Problems, in which he

argued that mechanics was less a natural philosophy than an man-made one, and was

22 Henri de Monantheuil, Aristotelis Mechanica (Paris: Ieremiam Perier, 1599) pp. 82–90; Giuseppe Biancani, Aristotelis loca mathematica ex universes ipsius operibus collecta et explicate (Bologna: Bartholomaeum Cochium, 1615) pp. 159–168. Biancani actually copied Nunes’ results verbatim, stating that the Portuguese mathematician had developed the “finest, most accurate and most meritorious” explanation of the Aristotelian problems (p. 162). 23 Bernardino Baldi, In mechanica Aristotelis problemata exercitationes (Mainz: Viduae Ioannis Albini, 1621) pp. 60–76. Baldi’s work is analyzed by Ludwig Rank in Die Theorie des Segelns in ihrer Entwicklung: Geschichte eines Problems der nautischen Mechanik (Berlin: Dietrich Reimer Verlag, 1984) pp. 33–35.

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therefore a fundamentally mathematical discipline.24 He extensively covered the

problems of naval architecture in 30 dense and well-illustrated pages, explicitly basing

his analysis on the works of Nunes and Baldi. Of particular interest is Guevara’s analysis

of Question 7, on the effect of the forward and after parts of the sail on the ship’s

maneuvering. In Guevara’s view, a lateen sail (a triangular sail with the highest part aft of

the mast) would tend to billow out before the wind, causing a change in the angle of

incidence to the wind between the forward part and the after part of the sail. Guevara

argued that the after part of the sail would, like an open bag, capture more wind (in

modern terms, the pressure point of the sail moves aft), thereby interfering more with the

rudder; hence sailors will take in the after part of the sail first to improve

maneuverability.25 The “wind bag” model of the sail was further extended by the Jesuit

mathematician Honoré Fabri (1607–1688), in his monumental Physica published in 1669.

Fabri, drawing on the analysis of Guevara, argued that a sail transfers its energy to the

ship because it is pliable and holds the wind; if it were flat then the wind would bounce

off it. For the sails to hold the wind, however, they must be porous like a bird’s wing,

which he assumed let air through the feathers in order to fly.26

24 Giovanni di Guevara, In Aristotelis mechanicas commentarii: una cum additionibus quibusdam ab eandem materiam pertinentibus (Rome: Mascardus, 1627) p. 5. 25 ibid, pp. 90–129. Guevara’s work is analyzed by Rank in Die Theorie des Segelns, pp. 72–75. 26 Honoré Fabri, Physica, id est, scientia rerum corporearum, 4 vol. (Lyon: Laurent Anisson, 1669) vol. 3 pp. 471–472. Fabri’s work is analyzed by Rank in Die Theorie des Segelns pp. 74–76. This “wind bag” model of the sail was further expanded by Johann and Jakob Bernoulli in the 1690s, and in the mid-1700s by Leonhard Euler; the model remained current through the early 1900s, when aerodynamic theory became systematically applied to sail design (see Julián Simón Calero, The Genesis of Fluid Mechanics, 1640–1780 (Dordrecht: Springer, 2008) pp. 254–264).

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5. ARISTOTLE AND THE PROBLEM OF BUOYANCY IN LATE RENAISSANCE AND JESUIT MECHANICS, 1611–1673

Although Mechanical Problems proved to be the principal focus for the efforts of natural

philosophers examining naval architecture during the late Renaissance and early part of

the Scientific Revolution, they also wrestled with another “maritime” aspect of the

Aristotelian corpus that was at odds with observed facts; the problem of buoyancy,

specifically the rationale for why a solid body floats in water. Aristotle had argued that

the properties of floating and sinking were due to the relative weight of the material in

each medium, as well as the shape of the body. In De Caelo (On the Heavens), he

extensively discussed the concepts of lightness and heaviness of objects; and in a final

chapter, he briefly stated the reasons why an object floats upon water:

In air, for instance, a talent’s weight of wood [about 26 kg] is heavier than a

mina of lead [about 0.4 kg] but in water the wood is lighter… the reason why

broad things keep their place is because they cover so wide a surface and the

greater quantity is less easily disrupted. Bodies of the opposite shape sink

down because they occupy so little of the surface, which is therefore easily

parted.27

In conflict with Aristotle’s explanation was the principle developed by Archimedes: an

object will float if it displaces a volume of water equal to or greater than its weight.

Although many scientists—and even some shipbuilders—had long since adopted

Archimedes’ model, the debate between these two theories was still so contentious that in

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the year 1611 Galileo found himself refuting Aristotle’s “shape theory” in favor of a

more Archimedean explanation involving the density of floating bodies, over the course

of a now-famous three-day discussion of the matter which he recorded in Discourse on

Floating Bodies (1612).28

This discourse, along with the well-known elucidations of Archimedes’ hydrostatic

principles by Simon Stevin and Blaise Pascal, helped to fundamentally shift scientific

sentiment away from Aristotle and towards Archimedes during the mid-seventeenth

century.29 However, Aristotle still held sway in the philosophy of the Jesuit academies,

which were arguably the most influentail educational system in Europe at the time. The

Jesuit curriculum outlined in the Ratio Studiorum, the plan of studies employed by its

network of schools across Europe and around the world, leaned heavily on Aristotelian

writings in the fields of mathematics and mechanics, including Physics, De Caelo and

Mechanical Problems. The study of mechanics as a “mixed science” (i.e., combining

principles of both “pure” mathematics and “practical” physics”) included collisions,

fluids, hydrostatics and the motion of bodies in resisting media, all of which found a

home in the nascent field of naval architecture.

27 Aristotle, The Complete Works of Aristotle, ed. Jonathan Barnes (Princeton: Princeton University Press, 1984), 312–313a, at pp. 402–405. 28 See Stillman Drake, Cause, Experiment and Science: A Galilean Dialogue Incorporating a New English Translation of Galileo's "Bodies That Stay atop Water, or Move in It" (Chicago: University of Chicago Press, 1981); and Paolo Palmieri, “The Cognitive Development of Galileo’s Thoery of Buoyancy”, Archive for the History of Exact Sciences 59 (2005), pp. 189–222. 29 Simon Stevin, Beghinselen des Waterwichts (Leyden: C. Plantijn, 1586) and Blaise Pascal, Traité de l'équilibre des liqueurs, et de la pesanteur de la masse de l'air (Paris: Guillaume Desprez, 1663).

18

Honoré Fabri (mentioned above) was not the first Jesuit to extend Aristotelian mechanics

into the realm of naval architecture, nor was it unusual that a Catholic priest, ostensibly

focused on matters of theology, be so deeply immersed in such secular concerns. Jesuit

professors were at the forefront of commenting and expanding upon these works, often

writing conflicting interpretations that fueled free and lively debates both inside and

outside the Jesuit community.30 Starting in 1623, several Jesuit colleges in France began

teaching hydrography, a subject that included navigation and piloting as well as ship

design and construction. The first major work on the subject, Hydrographie contenant la

théorie et la pratique de toutes les parties de la navigation, written in 1643 by the Jesuit

mathematics professor at La Flèche and Clermont, Georges Fournier (1595–1652),

included a substantial discourse on naval architecture.31

However, the Jesuit curriculum continued to place Aristotle on a pedestal, and he would

not be easily dislodged. For example, when Georges Fournier attempted to explain why a

ship floats in Hydrographie, he continued to mix Archimedean principles (i.e., correctly

asserting that the displacement of a ship equals the weight of the water that it pushes

30 William A. Wallace, Galileo and his Sources: The Heritage of the Collegio Romano in Galileo’s Science (Princeton: Prnceton University Press, 1984), pp. 202–209; James G. Lennox, “Aristotle, Galileo and ‘Mixed Sciences’”, in Reinterpreting Galileo, ed. William A. Wallace (Washington D.C.: Catholic University of America Press, 1986), pp. 29–51; Marcus Hellyer, Catholic Physics: Jesuit Natural Philosophy in Early Modern Germany (Notre Dame: University of Notre Dame Press, 2005), pp. 83–84, 119–122; Domenico Bertoloni Meli, Thinking with Objects: The Transformation of Mechanics in the Seventeenth Century (Baltimore: Johns Hopkins University Press, 2006), pp. 6–7. 31 Georges Fournier, Hydrographie, contenant la theorie et la pratique de toutes les parties de la navigation (Paris: Michel Soly, 1643; Jean Dupuis, 1667; reprint Grenoble : Edition des 4 Seigneurs, 1973). On Fournier, see Michel Vergé-Franceschi, Marine et Education sous l’Ancien Régime (Paris : CNRS, 1991) pp. 210–211; and Antonella Romano, “Teaching Mathematics in Jesuit Schools”, in The Jesuits II: Cultures, Sciences and the Arts, 1540–1773, ed. John W. O’Malley et al. (Toronto: University of Toronto Press, 2006) pp. 355–370, at pp. 362–364.

19

aside) with such Aristotelian concepts as there being a difference in the weight of

material according to the medium it inhabits:

There is a difference in the weight of the parts that are in the water and those

in the air….the same piece [of the ship] may be partly in water and partly in

air, and the part in the water weights less. …For all these reasons and others, I

conclude that it is moralement impossible [impossible by rational standards]

to be able to precisely determine and give general practice by which one can

know the force which would support a vessel. Also, I know of no

mathematician who has attempted this, even none who has proposed the

question.32

Nevertheless, at the same time Fournier was explaining in scholarly terms why the

displacement of ships could not be measured, naval constructors across the English

Channel, unencumbered by Jesuit philosphies, were in fact routinely doing just that.

Anthony Deane, in the best-known example, applied the principles of Archimedes to

paper drawings of hull curves (such drawings where then coming into vogue in England,

but were still almost unknown in France) to graphically calculate a warship’s immersed

volume, displacement and draft in order to ensure that gunports would be sufficiently

high above the waterline so they would not flood while under sail.33 This was a very

practical calculation that required only rudimentary arithmetic; but as yet, this did not

32 Fournier, Hydrographie pp. 608–609, 612–614. 33 Anthony Deane (ed. Brian Lavery), Deane’s Doctrine of Naval Architecture 1670 (London: Conway Maritime Press, 1981), pp. 7–20.

20

represent an attempt to extend Archimedes’ mathematical principles into an overall

science of ship design.

6. THE APOGEE OF ARISTOTELIAN NAVAL ARCHITECTURE IN THE FRENCH NAVY AND THE WORKS OF PAUL HOSTE, 1685–1700

The first tentative ventures into developing a science of ship design based on

mathematical theories occurred during the reign of Louis XIV, when the moribund

French navy, under the ministry of Jean-Baptiste Colbert (1619–1683), was rebuilt to

compete with the powerful English navy. Colbert, who famously created the Paris

Academy of Sciences to bolster French commerce and policy, also turned to science as a

way to make every French ship better than its English counterpart. Colbert and his

successors sponsored scientific research on naval architecture, including a famous series

of experiments conducted in the Grand Canal at Versailles to test mathematically-based

shipbuilding theories.34 At the same time, a series of schools were created to

professionalize the naval officers who would man the warships. The Ecoles des Gardes

de la Marine (cadet academies) were established in the dockyards of Rochefort, Brest and

Toulon, incorporating practical training in gunnery and fencing with theoretical

instruction in mathematics, fortifications and hydrography, with instruction by Jesuit

professors.

One such professor was Paul Hoste (1652–1700), a mathematician born on May 19, 1652

in Pont-de-Veyle in Bresse, about 400 km south of Paris. He attended the Jesuit college

in the town, and was admitted into a Jesuit seminary around 1669 at age 17. In 1685 at

34 Larrie D. Ferreiro, Ships and Science: The Birth of Naval Architecture in the Scientific Revolution, 1600–1800 (Cambridge: MIT Press, 2007) pp. 51–112.

21

age 33, he was appointed as professor of mathematics and hydrography at the newly-

formed Ecole des Gardes de la Marine in Toulon. While there, he met Admiral Anne-

Hilarion de Cotentin, comte de Tourville (1642–1701), with whom he would later serve

as chaplain.35 Tourville took a keen interest in Hoste’s scientific and mathematical ideas,

and sponsored a series of experiments to confirm Hoste’s concept that a ship having a

hemispherical bow and stern would be faster than a conventional hull form. Though the

model tests were inconclusive, Tourville encouraged Hoste to continue with his research

on mathematics, which the Jesuit soon applied to the principles of naval warfare.36

As chaplain aboard Tourville’s ships, Hoste witnessed naval warfare first-hand, including

the battle of La Hogue in 1692 where he survived the burning and sinking of the flagship

Soleil Royale. In 1697 Hoste collaborated with Tourville to a produce a groundbreaking

and widely-read book on naval tactics, L’Art des Armées Navales, which combined the

admiral’s fighting instructions with the neat geometry of the mathematics professor.

Appended to the text was a shorter work on naval architecture, Théorie de la construction

des vaisseaux, where at Tourville’s express orders, he elaborated on his mechanical

theories of ship design and performance. Yet these published ideas were incomplete, for

he was working on the manuscript of a second book, titled Architecture navalle, when he

died prematurely on February 23, 1700, not quite 48 years of age.37

35 Louis-Gabriel Michaud, Biographie universelle ancienne et moderne (Paris: Desplaces, 1854–1865), vol. 20 pp. 28–29. 36 Paul Hoste published a mathematics textbook Recueil des traités de mathématique (Lyon: Anisson) in 1692. 37 Paul Hoste, L’Art des Armées Navales ou Traité des Evolutions Navales, appended with Théorie de la construction des vaisseaux (Lyon: Anisson and Posuel, 1697); Paul Hoste, Architecture navalle, ou pratique de la construction des vaisseaux, copied by Jean Baptiste Thioly (Service Historique de la Marine à Vincennes, cote SHM ms.138, 1714).

22

Taken together, Théorie de la construction des vaisseaux and Architecture navalle

represent the apogee of the Aristotelian heritage in early naval architecture. They were

the first synthetic works on the subject, linking ship theory with practical shipbuilding

(for example, directly relating the effects of fluid resistance on hull form; Hoste argued

that since spheres and hemispheres had the lowest surface-area-to-volume ratio of any

solid, they had the least resistance, which is why his ship models had round ends).38 At

the same time, these works combined the mechanics of both Aristotle and Archimedes to

explain and quantify the behavior of ships.39 Hoste’s analyses of ship theory were a

complete departure from his predecessors, for two reasons: first, instead of providing

mere “handwaving arguments”, he developed mathematical equations which could be

analyzed to give direct numerical results; and second, rather than limiting himself to

discourses on rowing and the position of oars based on the Mechanical Problems, he

analyzed the problems of sailing warships, which were now the main concern for modern

navies.40 For example, in 1664 the 54-gun Lune had broken apart and foundered just off

Toulon with the loss of over 500 men, a disaster later (incorrectly) blamed on loss of

38 Hoste, Théorie de la construction des vaisseaux, pp. 8, 12–13, 23–28, 41–45; and Architecture navalle, pp. 11–12. 39 Hoste was by no means the first to combine elements of both Aristotle and Archimedes in a synthetic model of mechanics. Giovanni di Guevara, in his 1627 In Aristotelis mechanicas commentarii, combined Aristotle’s observations on the nature and properties of the circle, with other relating to center of gravity as developed by Archimedes and others (Wallace, Galileo and his Sources, p. 209). 40 This is not to say that the problems of rowing were completely abandoned by mathematicians after the Aristotelian problems fell out of vogue. For example, in 1749 Leonhard Euler devoted a long and complex chapter in his magisterial work Scientia navalis to the analysis of rowing and the action of oarsmen, using more analytical methods that accounted for mechanical forces and material strength of the oars, and the limits of mechanical power that can be generated by individual oarsmen (Leonhard Euler, Scientia Navalis, seu tractatus de construendis ac dirigendis navibus pars prior complectens theoriam universam de situ ac motu corporum aquae innatantium (Saint Petersburg: Saint Petersburg Academy of Sciences, 1749), Pars Secunda Caput VII, “De actione remorum”, pp. 291–352).

23

stability. Paul Hoste used this catastrophe to introduce his discourse on the theory of ship

design, stating “there is no greater fault than a vessel which cannot carry sail”.41

Hoste’s examination of ship stability, the “ability to carry sail”, demonstrates the sublime

mix of Aristotelian and Archimedean mathematics that marked his entire corpus. He

began by explaining, like Anthony Deane before him, the importance of calculating the

displacement of a ship to ensure that the gunports sufficiently high above the water. He

then demonstrated just how far the Jesuit curriculum had advanced since the time of

Fournier, when instead of complaining that it was moralement impossible to calculate

displacement, he actually provided several methods to do so, all based on the same solid

understanding of Archimedean principles as Deane: moreover, Hoste not only explained

how graphically to calculate the volume and displacement of a ship based on drawings,

but also provided methods to calculate the volume and displacement of actual ships by

measuring them from the outside.42

Hoste went on to explain that the moment (he used the term “force”) the ship must have

in order to properly carry sail, is that which it needs to resist the sail overturning moment.

He defined this moment as the the product of the the wind-on-sail force times the speed

of the mast rotation – in other words, he employed Aristotle’s lever law (Fv = fV), rather

than Archimedes’ lever law (Fl = fL). He went on to state in direct mathematical terms

how to determine the stability of the ship:

41 Hoste, Théorie de la construction des vaisseaux, p. 46. 42 ibid, p. 48; Hoste, Architecture navalle, pp. 1–10.

24

If one knows the center of gravity of the vessel, one easily can find the force it has

to carry sail, which is nothing less than the product of the weight of the vessel

times the distance of the centers [of weight and displacement].43

Or, in modern terms:

righting moment = Δ (BG)

where

Δ = displacement (weight) of ship

B = center of displacement

G = center of gravity

BG = distance from B to G

Although he did not provide a theoretical means for determining this “force to carry sail”,

he did furnish a procedure that could empirically demonstrate this—the inclining

experiment, which tangibly demonstrates stability by measuring the effect of a weight

hung over the side. Hoste asserted that, by measuring the angle of inclination of the ship

due to suspending a weight M from a boom at a certain height, that the “force to carry

sail” can be determined.44 In Hoste’s geometry using Figure 2, the center of displacement

B is the fulcrum, so that:

inclining moment = righting moment

M x BF = Δ x BA

43 Hoste, Théorie de la construction des vaisseaux, pp. 49, 54. 44 ibid, pp. 55–59.

25

He therefore arrived at the following equation for the force to support sail :

Δ BA = BANsinM∠

(BA+AF)

Or in modern notation:

Δ BG = θsin

W BF

Figure 2

Hoste’s diagram of an inclining experiment

(Hoste, Théorie de la construction des vaisseaux, figure 57)

There were several problems with this theorem, most notably that it leads to the

conclusion that the higher the center of gravity of the ship, the more stable it is, which is

of course the opposite of what actually happens. Nevertheless, it represented the first

attempt to develop a theoretical basis for ship stability, and was perhaps one of the few

examples where Aristotelian principles found a direct expression in mathematical

mechanics.

26

7. CONCLUSION: THE DOWNFALL OF ARISTOTELIAN MECHANICS AND THE RISE OF NEWTONIAN NAVAL ARCHITECTURE, 1727–1746

Paul Hoste’s works were was the first true synthesis of naval architecture that treated the

ship as a complete system, and would remain the only such work for almost half a

century. Although they were enormously influential, they were already obsolete when

written, for they appeared just as Isaac Newton’s Principia Mathematica (1687) was

starting to find acceptance. It was an awkward era, when mathematicians and scientists

attempted to somehow fuse old and new concepts, as did Hoste when he combined

Aristotle and Archimedes to explain ship stability. This combination of two disparate

theories at first led the French hydrographer Pierre Bouguer (1698–1758) astray when

wrote a prize-winning treatise for the Paris Academy of Sciences on the masting of ships

in 1727. To explain ship stability – a critical concept of naval architecture that was still

poorly understood—he invoked Hoste’s “force to carrying sail”, which was founded on

Aristotelian precepts of the lever, while at the same time mixing in Archimedean lever

laws to explain the shift in buoyancy when a ship heels over. This combination of

Aristotelian and Archimedean mechanics proved unsuccessful in providing a meaningful

theory of ship stability.45

In 1746, however, Bouguer published his breakthrough work Traité du navire in which

he cast aside the Aristotelian tradition, developing a complete synthesis of ship theory

based solely on the mechanics of Archimedes and the mathematics of Isaac Newton,

providing a set of tools that allowed naval constructors to predict how their ships would

45 Pierre Bouguer, De la mâture des vaisseaux (Paris: Claude Jombert,1728) pp. 24–25.

27

float and sail. Among the most durable concepts was his development of a complete

theory of stability using a concept known as the metacenter, which remains the basis for

modern stability theory. But perhaps something of Aristotle yet remains, for Bouguer also

provided us with the practical method for verifying stability: the inclining experiment,

little changed from Hoste’s first elucidation, which modern naval architects across the

globe routinely use to verify that a ship is safe and ready to sail.46

46 Pierre Bouguer, Traité du Navire, de sa Construction, et de ses Mouvemens (Paris: Claude Jombert,1746), pp. 199–324. For a complete survey of the development of ship stability theory, see Ferreiro, Ships and Science pp. 157–257.

28

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339 Soph i a Vac k imes & Kons t an ze We l t e r sbach ( eds . ) Wandering seminar on scientif ic Objects

340 U l j a na Fees t , G i o r a Hon , Hans - Jö rg Rhe i nbe rge r, J u t t a Sch i c k o r e , F r i e d r i c h S t e i n l e ( eds . ) generating experimental knowledge

341 S í l v i o R . Dahmen Boltzmann and the art of flying

342 Gerha rd He r rgo t t Wanderer -fantasien. franz liszt und die figuren des Begehrens

343 Con f e r ence a cultural history of heredity IV: heredity in the century of the gene

344 Kar i n e Chem la canon and commentary in ancient china: an outlook based on mathematical sources

345 Omar W. Nas im Observations, Descriptions and Drawings of nebulae: a sketch.

346 Ju l i a Ku rse l l ( e d . ) sounds of science – schall im labor (1800–1930)

347 Soph i a Vac k imes the genetically engineered Body: a cinematic context

348 Lu i g i Gue r r i n i the ‘accademia dei lincei’ and the new World.

349 Jens Høy r up über den ital ienischen hintergrund der rechenmeister -Mathematik

350 Chr i s t i a n Joas , Ch r i s t oph Lehne r, a nd Jü rgen Renn ( eds . ) hQ-1: conference on the history of Quantum Physics (Vols. I & II)

351 José M . Pacheco Does more abstraction imply better understanding? ( “Apun t es de Mecán i c a Soc i a l ” , b y An t on i o Po r t uondo )

352 José M igue l Pacheco Cas t e l a o , F. J a v i e r Pé re z - Fe r nánde z , Ca r l o s O . Suá re z A l emán following the steps of spanish Mathematical analysis: from cauchy to Weierstrass between 1880 and 1914

353 José M igue l Pacheco Cas t e l a o , F. J a v i e r Pé re z - Fe r nánde z , Ca r l o s O . Suá re z A l emán Infinitesimals in spain: antonio Portuondo’s Ensayo sobre el Infinito

354 A lbe r t P r esas i Pu i g reflections on a peripheral Paperclip Project: a technological innovation system in spain based on the transfer of german technology

355 A lbe r t P r esas i Pu i g the contribution of the history of science and social studies to the understanding of scientif ic Dynamics: the case of the spanish nuclear energy Program

356 Vi o l a Ba l z , A l e x ande r v. S chwer i n , He i k o S t o f f , Be t t i n a Wahr i g ( eds . ) Precarious Matters / Prekäre stoffe. The H i s t o r y o f Dange rous and Endange red Subs t ances i n t h e 19 th and 20 th Cen t u r i e s

357 F l o r en t i n a Bada l a no va Ge l l e r Qur’ān in vernacular. Fo l k I s l am i n t h e Ba l k ans

358 Rena t e Wahsne r & Ho rs t -He i n o v. Bo r z es z kowsk i Die naturwissenschaft und der philosophische Begriff des geistes

359 Jens Høy r up Baroque Mind-set and new science. A D i a l e c t i c o f Se ven t een t h -Cen t u r y H i gh Cu l t u r e

360 D i e t e r F i c k & Ho rs t Kan t Walther Bothe’s contributions to the particle-wawe dualism of l ight

361 A lbe r t P r esas i Pu i g ( ed . ) Who is Making science? scientists as Makers of technical-scientif ic structures and administrators of science Policy

362 Chr i s t o f W indgä t t e r Zu den akten – Verlags- und Wissenschaftsstrategien der Wiener Psychoanalyse (1919–1938)

363 Jean Pau l Gaud i l l i è r e a nd Vo l k e r Hess ( eds . ) Ways of regulating: therapeutic agents between Plants, shops and consulting rooms

364 Ange l o Ba racca , L eopo l do Nu t i , J ü rgen Renn , Re i n e r B raun , Ma t t eo Ge r l i n i , Mar i l e na Ga l a , a nd A l be r t P r esas i Pu i g ( eds . ) nuclear Proliferation: history and Present Problems

365 Vi o l a v an Bee k „Man lasse doch diese Dinge selber einmal sprechen“ – experimentierkästen, experimentalanleitungen und erzählungen um 1900

366 Ju l i a Ku rse l l (H rsg . ) Physiologie des klaviers. Vor t r äge und Kon ze r t e z u r W issenscha f t sgesch i c h t e d e r Mus i k

367 Hube r t L a i t k o strategen, Organisatoren, kritiker, Dissidenten – Verhaltensmuster prominenter naturwissenschaftler der DDr in den 50er und 60er Jahren des 20. Jahrhunderts

368 Rena te Wahsne r & Ho rs t -He i n o v. Bo r z es z kowsk i naturwissenschaft und Weltbild

369 D ie t e r Ho f fmann , Ho l e Röß l e r, Ge ra l d Reu t he r „lachkabinett“ und „großes fest“ der Physiker. Walter grotrians „physikalischer einakter“ zu Max Plancks 80. geburtstag.

370 Shau l Ka t z i r from academic physics to invention and industry: the course of hermann aron’s (1845–1913) career